492
8 Morphogenesis
This idea is consistent with a wide range of experiments conducted by Beloussov
and colleagues (Beloussov 1998, 2015). In one particularly interesting example, a
piece of epithelium initially under tension is extracted from an embryo and cultured
in isolation. How can the tension be (hyper) restored if no constraints are present to
prevent the sample from remaining stress free when it contracts in response to the
decreased tension? Nature solves this problem as follows. First, the membrane rolls
up into a fluid-filled spherical shell, and then osmosis generates cavity pressure that
creates tension in the wall (Beloussov 1998).
Although some exceptions exist, HR also is consistent with experiments conducted in other laboratories. For example, the early embryonic heart and brain are
fluid-filled tubes that are normally compressed by external tissues. Like squeezing
a fluid-filled balloon, these loads increase wall tension. When the external tissues
are removed, the walls of both organs contract, presumably to raise the stress back
toward normal levels. Moreover, if the samples are then artificially compressed, they
relax again to reduce tension (Filas et al. 2011).
Beloussov (1998) speculates that, as in the model of Odell et al. (1981), a local
mechanical perturbation, possibly modulated by genetic activity, causes a local HR
response that perturbs stress in neighboring cells, which then undergo their own
HR response, and so on, until the proper form is created. This sequence of events
transfers some of the regulatory work from the genes to the cytoskeleton, which
then act together through feedback to minimize morphogenetic abnormalities. In
fact, recent experiments show how mechanical interactions can drive a series of
shape changes in the Drosophila embryo (Merle and Farge 2018).
8.9.2 Morphomechanical Laws
To capture the HR response mathematically, we begin with the 1D growth law
˙
G = a(σ − σ 0 )G,
(8.76)
where a is a positive constant, and σ 0 is the target (homeostatic) stress. One way to
get an overshoot is through a delayed response, like using a heater with a thermostat
to control room temperature. Another is by genes specifying changes in σ 0 following
a mechanical perturbation, e.g., an increase in σ 0 would follow a drop in stress. 20
This approach produces well-controlled shape changes (Ramasubramanian and
Taber 2008), but is inconsistent with the premise that mechanical feedback can
sometimes control the response without direct genetic intervention.
20 Similarly, to obtain realistic growth in a developing artery, we earlier assumed that the target
stresses increase with blood pressure [see Eq. (6.128)].
8 Morphogenesis
This idea is consistent with a wide range of experiments conducted by Beloussov
and colleagues (Beloussov 1998, 2015). In one particularly interesting example, a
piece of epithelium initially under tension is extracted from an embryo and cultured
in isolation. How can the tension be (hyper) restored if no constraints are present to
prevent the sample from remaining stress free when it contracts in response to the
decreased tension? Nature solves this problem as follows. First, the membrane rolls
up into a fluid-filled spherical shell, and then osmosis generates cavity pressure that
creates tension in the wall (Beloussov 1998).
Although some exceptions exist, HR also is consistent with experiments conducted in other laboratories. For example, the early embryonic heart and brain are
fluid-filled tubes that are normally compressed by external tissues. Like squeezing
a fluid-filled balloon, these loads increase wall tension. When the external tissues
are removed, the walls of both organs contract, presumably to raise the stress back
toward normal levels. Moreover, if the samples are then artificially compressed, they
relax again to reduce tension (Filas et al. 2011).
Beloussov (1998) speculates that, as in the model of Odell et al. (1981), a local
mechanical perturbation, possibly modulated by genetic activity, causes a local HR
response that perturbs stress in neighboring cells, which then undergo their own
HR response, and so on, until the proper form is created. This sequence of events
transfers some of the regulatory work from the genes to the cytoskeleton, which
then act together through feedback to minimize morphogenetic abnormalities. In
fact, recent experiments show how mechanical interactions can drive a series of
shape changes in the Drosophila embryo (Merle and Farge 2018).
8.9.2 Morphomechanical Laws
To capture the HR response mathematically, we begin with the 1D growth law
˙
G = a(σ − σ 0 )G,
(8.76)
where a is a positive constant, and σ 0 is the target (homeostatic) stress. One way to
get an overshoot is through a delayed response, like using a heater with a thermostat
to control room temperature. Another is by genes specifying changes in σ 0 following
a mechanical perturbation, e.g., an increase in σ 0 would follow a drop in stress. 20
This approach produces well-controlled shape changes (Ramasubramanian and
Taber 2008), but is inconsistent with the premise that mechanical feedback can
sometimes control the response without direct genetic intervention.
20 Similarly, to obtain realistic growth in a developing artery, we earlier assumed that the target
stresses increase with blood pressure [see Eq. (6.128)].